Total cost minimization in smart grids with unknown objective function

Document Type : Original Article

Authors

School of Advanced Technologies, Shiraz University, Shiraz, Iran

Abstract

Smart grids are complex, nonlinear and uncertain systems. Smart grids may consist of one or more cost functions, in which their optimal values have to be obtained. Moreover. In these systems the optimal condition has to be find with small computation burden, high accuracy, and relatively fast in real time. In this paper, a novel approach is proposed to find the minimum value of the total cost for the energy consumption in smart grids, in which the total cost is considered as uncertain objective function. The advantages of this technique are its stability, fast convergence, insensitivity with respect to initial condition and real time implementation. Some simulation results are provided to show the effectiveness of the proposed approach.

Keywords


[1] M. Guay, V. Adetola, "Adaptive economic optimizing model predictive control of uncertain nonlinear systems", International Journal of Control, vol. 86, no. 8,  pp. 1425-1437, 2013.
[2] Y. Tan, D. Nesic, I. Mareels, "On non-local stability properties of extremum seeking control", Automatica, vol. 42, no. 6, pp. 889-903, 2006.
[3] M. Krstic, H. H. Wang, "Stability of extremum seeking feedback for general nonlinear dynamic systems", Automatica, vol. 36, no. 4, pp. 595-601, 2000.
[4] M. Krstic, "Performance improvement and limitations in extremum seeking control", Systems and Control Letters, vol. 39, no. 5, pp. 313-326, 2000.
[5] M. Guay, T. Zhang, "Adaptive extremum seeking control of nonlinear dynamic systems with parametric uncertainties", Automatica, vol. 39, no. 7, pp. 1283-1293, 2003.
[6] Y. Tan,  D. Nesic, I. Mareels, "On the choice of dither in extremum seeking systems: A case study", Automatica, vol. 44, no. 5, pp. 1446-1450, 2008.
[7] Y. Tan, D. Nesic, I. Mareels, A. Astolfi, "On global extremum seeking in the presence of local extrema", Automatica, vol. 45, no. 1, pp. 245-251, 2009.
[8] A. Ghaffari, M. Krstic, D. Nesic, "Multivariable Newton-based extremum seeking", Automatica, vol. 48, no. 8, pp. 1759-1767, 2012.
[9] Y. Tan, Y. Li, I. Mareels, "Extremum seeking for constrained inputs", IEEE Transactions on Automatic Control, vol. 58, no. 9, pp. 2405-2410, 2013.
[10] M. Haring, T. A. Johansen, "Asymptotic stability of perturbation-based extremum-seeking control for nonlinear plants", IEEE Transactions on Automatic Control, vol. 62, no. 5, pp. 2302-2317, 2017.
[11] R. Suttner, "Extremum seeking control with an adaptive dither signal", Automatica, vol. 101, pp. 214-222, 2019.
[12] D. Bhattacharjee, K. Subbarao, "Extremum seeking control with attenuated steady-state oscillations", Automatica, vol. 125, 2021.
[13] A. Kebir, L. Woodward, O. Akhrif, "Real-time optimization of renewable energy sources power using neural network-based anticipative extremum-seeking control", Renewable Energy, vol. 134, pp. 914-926, 2019.
[14] L. Hu, F. Xue, Z. Qin, J. Shi, W. Qiao, W. Yang, T. Yang, "Sliding mode extremum seeking control based on improved invasive weed optimization for MPPT in wind energy conversion system", Applied Energy, vol. 248, pp. 567-575, 2019.
[15] T. I. Salsbury, J. M. House, C. F. Alcala, "Self-perturbing extremum-seeking controller with adaptive gain", Control Engineering Practice, vol. 101, 2020.
[16] M. Guay, D. Dochain, "A time-varying extremum-seeking control approach", Automatica, vol. 51, pp. 356-363, 2015.
[17] M. Guay, E. Moshksar, D. Dochain, "A constrained extremum-seeking control approach", International Journal of Robust and Nonlinear Control, vol. 25, no. 16, pp. 3132-3153, 2015.
[18] E. Moshksar, M. Guay, "Estimation-based approach for real-time optimisation of uncertain nonlinear systems", International Journal of Control, vol. 90, no. 9, pp. 2005-2019, 2017.
[19] M. W. Hirsch, C. C. Pugh, M. Shub, "Invariant Manifolds, 1st edition", Springer Berlin, Heidelberg, 1977.
[20] R. Abe, H. Taoka, D. McQuilkin, "Digital grid: communicative electrical grids of the future", IEEE Transactions on Smart Grid, vol. 2, no. 2, pp. 399-410, 2011.
[21] A. Chis, V. Koivunen, "Coalitional Game-Based Cost Optimization of Energy Portfolio in Smart Grid Communities", IEEE Transactions on Smart Grid, vol. 10, no. 2, pp. 1960-1970, 2019.
[22] S. Javaid, Y. Kurose, T. Kato, T. Matsuyama, "Cooperative distributed control implementation of the power flow coloring over a nano-grid with fluctuating power loads", IEEE Transactions on Smart Grid, vol. 8, no. 1, pp. 342-352, 2017.
[23] D. Burmester, R. Rayudu, W. Seah, D. Akinyele, "A review of nanogrid topologies and technologies", Renewable and Sustainable Energy Reviews, 2017, vol. 67, pp. 760-775, 2017.
[24] E. Y. Song, G. J. FitzPatrick, K. B. Lee, E. Griffor, "A Methodology for Modeling Interoperability of Smart Sensors in Smart Grids" IEEE Transactions on Smart Grid, vol. 13, no. 1, pp. 555-563, 2022.
[25] M. Yu, et al., "Pricing Information in Smart Grids: A Quality-Based Data Valuation Paradigm" IEEE Transactions on Smart Grid, vol. 13, no. 5, pp. 3735-3747, 2022.
[26] M. Ye, G. Hu, "Distributed extremum seeking for constrained networked optimization and its application to energy consumption control in smart grid", IEEE Transactions on Control System Technology, vol. 24, no. 6, pp. 2048-2058, 2016.
[27] H. Yang, et al., "A Practical Pricing Approach to Smart Grid Demand Response Based on Load Classification" IEEE Transactions on Smart Grid, vol. 9, no. 1, pp. 179-190, 2018.
[28] Z. Amjad, et al., "Towards Energy Efficient Smart Grids Using Bio-Inspired Scheduling Techniques" IEEE Access, vol. 8, pp. 158947-158960, 2020.
[29] T. Lu, et al., "A Reinforcement Learning-Based Decision System for Electricity Pricing Plan Selection by Smart Grid End Users" IEEE Transactions on Smart Grid, vol. 12, no. 3, pp. 2176-2187, 2021.
]30[ امیررضا حسنی آهنگر، گئورگ قره پتیان، علی اصغر خدادوست آرانی، حسین عسکریان ابیانه، «تأثیرات توپولوژی شبکه سایبری بر روی قابلیت اطمینان شبکه هوشمند با درنظرگیری ارتباط مستقیم شبکه سایبر- قدرت»، مجله مهندسی برق دانشگاه تبریز، جلد 48، شماره 2، صفحات 573-584، 1397.
[31] حسین شایقی، علی قاسمی، «پیش­بینی قیمت روزانه برق با شبکه عصبی بهبود یافته مبتنی بر تبدیل موجک و روش آشوبناک جستجوی گرانشی»، مجله مهندسی برق دانشگاه تبریز، جلد 45، شماره 4، صفحات 105-115، 1394.
[32] نبی طاهری، رحمت الله هوشمند، رضا همتی، «برنامه­ریزی هماهنگ نصب منابع تولید پراکنده و توسعه شبکه توزیع در حضور نامعینی بار و قیمت انرژی»، مجله مهندسی برق دانشگاه تبریز، جلد 44، شماره 1، صفحات 43-56، 1393.
[33] مرتضی رجبی مندی، محمدابراهیم حاجی­آبادی، مجید بقائی­نژاد، «الگوریتمی ترکیبی بر پایه روشهای هوش محاسباتی جهت مدیریت مصرف برق خانگی با حضور خودروی برقی»، مجله مهندسی برق دانشگاه تبریز، جلد 48، شماره 2، صفحات 617-629، 1397.
[34] K. Ma, G. Hu, C. J. Spanos, "Distributed energy consumption control via real-time pricing feedback in smart grid", IEEE Transactions on Control Systems Technology, vol. 22, no. 5, pp. 1907-1914, 2014.
[35] A. Astolfi, R. Ortega, "Immersion and invariance: a new tool for stabilization and adaptive control of nonlinear systems", IEEE Transactions on Automatic Control, vol. 48, no. 4, pp. 590-606, 2003.
[36] C. Gao, J. Li, Y. Fan, W. Jing, "Immersion and invariance-based control of novel moving-mass flight vehicles", Aerospace Science and Technology, vol. 74, pp. 63-71, 2018. 
[37] Z-E. Lou, J. Zhao, "Viable immersion and invariance control for a class of nonlinear systems and its application to aero-engines", Journal of the Franklin Institute, vol. 356, no. 1, pp. 42-57, 2019. 
[38] E. Moshksar, M. Guay, "Almost invariant manifold approach for adaptive estimation of periodic and aperiodic unknown time‐varying parameters", International Journal of Adaptive Control and Signal Processing, vol. 30, no. 1, pp. 76-92, 2016.
[39] L. Yu, D. Xie, T. Jiang, Y. Zou, K. Wang, "Distributed Real-Time HVAC Control for Cost-Efficient Commercial Buildings Under Smart Grid Environment", IEEE Internet of Things Journal, vol. 5, no. 1, pp. 44-55, 2018.